Unless we're willing to throw out the whole New Testament, and much of it can indeed be thrown out, then there is one test which can be found within its pages to show there was probably an original founder of the Jesus cult. It's this: The criterion of embarrassment. It seems improbable to me that these writers invented a prediction of the eschaton to happen in their generation which had to continually be explained away because it never happened--that is, unless there was someone who initially predicted that the "Son of Man" in Daniel 7 was to return in his own day and era. As we date the books of the NT we see the goal posts continually being moved to allow this prediction to be put off until it becomes so watered down that the 2nd century epistle of 2nd Peter says "a day with the lord is like a thousand years."

There have been a plethora of millennial movements down through the ages and Jewish literature both before and afterward shows us they expected this event. So the existence of such a prophetic person seems to be a reasonable one. We have evidence that people in that period expected such an event. And we see from the criterion of embarrassment in the NT that later and later documents continued to explain away why it didn't happen as time moved on.

From this evidence we don't need extra-biblical evidence to support his existence, but the strongest extra-biblical evidence we have is Josephus who stated that James was the brother of Jesus (Antiquities 20,9,1).